1. Field of the Invention
The present invention relates to optical systems, in particular to photolithography tools, including a group of optical elements that each comprises a birefringent cubic crystal.
2. Description of Related Art
Photolithography tools are commonly used in the fabrication of electrical and optical integrated circuits for forming images of device patterns on semiconductor substrates. Since the resolving power of such tools is inversely proportional to the exposure wavelength, new generations of such tools generally use exposure light with a shorter wavelength than used by tools of the previous generation. At present, deep ultraviolet light having a wavelength of 248 nm is used for submicron lithography. The next generations of photolithography tools will use exposure light with wavelengths of 193 and even 157 nm.
One of the major problems encountered when using exposure light having such short wavelengths is the fact that conventional lens materials such as quartz crystals or glasses are not sufficiently transparent in the deep ultraviolet wavelength domain. Among the most promising materials that could one day completely replace conventional lens materials is a class of single crystal fluoride materials that have, for the wavelengths of interest, much higher transmittances than conventional lens materials. Thus far calcium fluoride (CaF2) seems to be the most promising candidate within this material class; other cubic crystals belonging to that class include barium fluoride, lithium fluoride and strontium fluoride.
Of prime concern for the use of cubic crystalline materials for optical elements in deep ultraviolet lithography tools is the anisotropy of refractive index that is inherent in cubic crystalline materials and commonly referred to as “intrinsic birefringence”. Since the intrinsic birefringence scales approximately as the inverse of the wavelength of light, the issue of birefringence becomes particularly significant if the exposure wavelength approaches 100 nm.
In birefringent materials, the refractive index varies as a function of the orientation of the material with respect to the direction of incident light and also of its polarization. As a result, unpolarized light propagating through a birefringent material will generally separate into two beams with orthogonal polarization states. When light passes through a unit length of a birefringent material, the difference in refractive index for the two ray paths will result in an optical path difference or retardance. The retardance causes wavefront aberrations that are usually referred to as “retardance aberrations” and are capable of significantly degrading image resolution and introducing distortion of the image field at the wavelength of interest.
One of the most interesting approaches for addressing the problem of retardance aberrations is to combine an optical system with several cubic crystals whose crystal lattices are oriented with respect to each other in such a way that the overall retardance is reduced by mutual compensation. The underlying idea is to exploit the fact that, if a first polarization state is retarded in one crystal, a second polarization state being orthogonal to the first one may be retarded in another crystal of the optical system. As a result, the retarded wavefront of the first polarization state may “catch up” with the wavefront of the second polarization state while the latter is retarded in the other crystal. The overall net retardance of both crystals, i.e. the difference between both retardances imposed on the different polarization states, may then be considerably reduced or even made to vanish.
In WO 02/093209 an optical system is described comprising two groups each including two lenses that are made of cubic crystals. In one group, two crystals forming the lenses are oriented such that each [111] crystal axis (or an equivalent crystal axis such as the [11-1] axis, for example) coincides with the optical axis that is defined as the symmetry axis of the optical system. The orientations of the crystal lattices of both crystals differ in that the crystal lattice of one of the crystals results from rotating the crystal lattice of the other crystal around the optical axis by 60°. As a result of this rotation that is often referred to as “clocking”, the rotational asymmetry of birefringence that is inherent to each single crystal is substantially reduced if taking the group as a whole.
Within the other group the two lenses are made of crystals whose crystal lattices are oriented such that each [100] crystal axis coincides with the optical axis of the optical system. Again, the crystal lattices are rotated around the optical axis, but in this case by only 45°. Also in this group the birefringences of both crystals combine such that the overall birefringence of the group is almost rotational symmetrical.
However, since the birefringences induced in both lens groups have different signs, different polarization states are retarded in each group. This opens the way for mutually compensating the effects of birefringence induced in both lens groups. As the birefringence in both lens groups differs in sign, but approximately equals in magnitude, rotational asymmetry and the overall retardance of the whole system comprising both lens groups can be significantly reduced if both polarization states travel the same path lengths within each crystal.
A similar approach is also disclosed in U.S. 2003/0011896 A1.
In both documents it is stated that the angular deviation between the optical axis and the crystal axis that is to coincide with the optical axis shall not exceed 4° or 5°. Apparently, deviations from perfect alignment are not desired and may, if they exceed certain limits, impede the advantageous effects intended by the proposed crystal lattice orientations.
However, as has been briefly mentioned above, a good compensation of the overall retardance induced by birefringence requires that the retardances induced in both lens groups affect orthogonal polarization states, but have the same magnitude. The magnitude of the retardance is determined by the product of birefringence and path length; thus, equal retardances can only be achieved if this product is, for a given light ray, constant in both lens groups. Since the birefringence itself is, in the case of cubic crystals, a function of the angle of incidence, not only the angular birefringence distribution, but also the path length and the angle of incidence have to be taken into account.
The same considerations also apply, mutatis mutandis, in those cases in which the design objective is not (or not exclusively) the reduction of overall retardance, but to positively affect the retardance or its angular pupil distribution for achieving other advantageous effects. For example, in many cases it is more desirable to have a particular symmetric angular retardance distribution than to achieve a minimum mean retardance. It then does not suffice to provide two crystals or crystal groups whose sum of the birefringence distributions is symmetrical. Instead, achieving a desired symmetry of the angular retardance distribution also requires taking into account the paths lengths and angles of incidence of light rays propagating through the optical elements. The desired retardance distribution generally depends on the properties of other polarization selective optical elements within the optical system, for example beam splitter coatings, anti-reflection coatings or quarter wave plates.
Unfortunately, the path lengths and angles of incidence of the rays through the lenses cannot be varied just at it would be required for achieving the desired retardance property. This is because the shape of the lenses, their arrangement within the optical system and thus also the optical paths taken by light rays when propagating through the lenses are almost completely determined by the design of the optical system as a whole in view of the imaging properties that are to be achieved.
As a result, these known approaches make it possible to considerably reduce, symmetrize or generally positively affect the retardance only in very restricted circumstances in which, for a given polarization state, the angles of incidence and the path lengths within the crystals have the necessary values. This considerably qualifies the application of these approaches.